title: Adaptive cornea modeling from keratometric data.
abstract: OBJECTIVE
  To introduce an iterative, multiscale procedure that allows for better reconstruction of the shape of the anterior surface of the cornea from altimetric data collected by a corneal topographer.
  
  
  METHODS
  The report describes, first, an adaptive, multiscale mathematical algorithm for the parsimonious fit of the corneal surface data that adapts the number of functions used in the reconstruction to the conditions of each cornea. The method also implements a dynamic selection of the parameters and the management of noise. Then, several numerical experiments are performed, comparing it with the results obtained by the standard Zernike-based procedure.
  
  
  RESULTS
  The numerical experiments showed that the algorithm exhibits steady exponential error decay, independent of the level of aberration of the cornea. The complexity of each anisotropic Gaussian-basis function in the functional representation is the same, but the parameters vary to fit the current scale. This scale is determined only by the residual errors and not by the number of the iteration. Finally, the position and clustering of the centers, as well as the size of the shape parameters, provides additional spatial information about the regions of higher irregularity.
  
  
  CONCLUSIONS
  The methodology can be used for the real-time reconstruction of both altimetric data and corneal power maps from the data collected by keratoscopes, such as the Placido ring-based topographers, that will be decisive in early detection of corneal diseases such as keratoconus.
authors.affiliation: Department of Statistics and Applied Mathematics, Almería University, Carreterade Sacramento s/n, Almería, Spain. andrei@ual.es
authors.forename: Andrei
authors.initials: A
authors.lastname: Martínez-Finkelshtein
authors.forename: Darío Ramos
authors.initials: DR
authors.lastname: López
authors.forename: Gracia M
authors.initials: GM
authors.lastname: Castro
authors.forename: Jorge L
authors.initials: JL
authors.lastname: Alió
mesh_terms: D000465:Algorithms; D019412:Anatomy, Cross-Sectional; D003315:Cornea / Q000033:anatomy & histology*; D019781:Corneal Topography; D006801:Humans; D008433:Mathematics; D008954:Models, Biological